Traditional silicon-based pressure sensors have reached maturity and are widely commercially available. They are generally limited to operation at temperatures of less than 200° C. due to technical limitations. Current technological improvements have yielded traditional sensors that can operate in temperatures of up to 500° C. and at pressures up to 50 MPa. Additionally, very few commercial units have been demonstrated to work in the body without foreign body response causing critical drift errors. There has also been no demonstration of micromachined pressure sensors that can sustain operation in long term caustic and radioactive environments such as those commonly found in the nuclear fuel cycle.
A typical interface-type sensor is shown in FIG. 1. A closed channel with liquid at the inlet forms a gas/liquid interface inside the channel. The channel is within a substrate and in fluid communication with the inlet. The volume of the gas in the channel is directly related to the pressure outside of the device due to hydraulic compression from the liquid. This relationship is approximately defined by the Van der Waals equation:
PV=NκT where P=pressure, V=volume, N=number of particles in the gas, κ=Boltzmann's constant, and T=temperature. The distance that the liquid is driven in (or out) of the channel is directly related to the pressure and temperature of the environment by the gas laws.
The device is initially “primed” at a fixed gas pressure (Po), temperature (To) and has an initial volume (Vo). A volume measurement is taken by one of several means (optically, capacitive, digitally, etc.) and the current pressure Pg is determined from the relative gas law equation (this equation can be modified to account for elements of Van der Waals equation if greater accuracy is required):
      P    g    =                    P        o            ⁡              (                              V            o                                V            g                          )              ⁢          (                        T          g                          T          o                    )      
By measuring volume, the pressure in the channel can be calculated. Then, the pressure outside of the substrate can be determined.
These laws work well with large channels where only the ambient pressure is of concern. FIG. 2 shows a small channel—a microchannel with a diameter of less than about 200 micrometers—within a substrate and having a liquid/gas interface. The FIG. 2 shows an atmospheric pressure from the inlet (or outlet) port to just prior to the meniscus curve, and a meniscus pressure from an “Ideal Point” to the “Meniscus Point”. This results in a measured pressure that is equal to the combination of the atmospheric pressure and the meniscus pressure.
The first deviation from operations governed by the previous equations is a pressure barrier that a meniscus creates inside the microchannel. There can be both advancing and receding meniscus' that sustain pressure drops, which creates hysteresis and measurement error. The capillary pressure (Pcap) created by a meniscus is given by a variant of the Young-Laplace equation:
      P    cap    =      2    ⁢    σ    ⁢                  ⁢    cos    ⁢                  ⁢          θ      ⁡              (                              1                          h              c                                +                      1                          w              c                                      )            where σ is the surface tension of the liquid and θ is the contact angle of the liquid on the surface. This yields a final measured pressure Pmeas that is related to the gas pressure Pg and the capillary pressure:
      P    meas    =            P      g        -          2      ⁢              σ        ⁡                  (                      cos            ⁢                                                  ⁢            θ                    )                    ⁢              (                              1                          h              c                                +                      1                          w              c                                      )            
The meniscus effect can limit the minimum detectable resolution of an oscillating pressure because the meniscus changes from an advancing contact angle to a receding contact angle when pressure changes cause the liquid to change from moving forward in the channel to receding and vice versa. A worst case scenario for this pressure resolution would be the combination of the values of the capillary (microchannel) pressure for both advancing and receding contact angles.
What is needed is a pressure sensor for a microchannel substrate apparatus that measures and cancels out of the final pressure measurement the meniscus pressure.